A pump transfers water from a lake to a rectangular (20m x 20m) reservoir. Water

Question

A pump transfers water from a lake to a rectangular (20m x 20m) reservoir. Water is discharged into a distribution network from this rectangular reservoir by means of a 1.05m-width weir carved on its side wall. The reservoir bottom, pump and weir crest elevations are 0.0, 1.0 and 6.0 m, respectively. The evaporation, E, and infiltration, I, in the reservoir can be expressed using the following equations below (depths in metres): E (-) = 0.01Wh day (-) = 0.05e10 day where, h is the water surface level in the reservoir The discharge of the rectangular weir [m3/s] can be expressed as follows where, Cw is the weir coefficient (Cw-1.83), w is weir width, and h is the head above the weir Qweir = Cww(Ah)1.5 crest The discharge of the pump [m/s] can be expressed as follows 17.5 pump where, H is the total water head above the pump discharge pipe. If the initial water surface level in the reservoir (ie, at = 0) s 8m, find the water level after 15 minutes of operation. Use as many time steps as required to get a smooth solution. It is recommended to use Excel.

Explanation / Answer

At t= 0, water surface level in the reservoir (h) = 8 m

So,

Evaporation (E) = 0.01 3h (m / day)

= 0.0138 = 0.02 (m/day)

For 15 min it will be = (0.02 x 15)/ 24 x 60

= 2.08 × 10-4 m

So, Total evaporation from Reservoir = 2.08 x 10-4 x 20 x 20

= 0.083m3

Infiltration (I) = 0.05 e(h/10)

. = 0.05 e(8/10)

. = 0.11 (m/day)

For 15 min it will be = (0.11 x 15)/24 x 60

= 1.16 x 10-3 m

So, Total infiltration from Reservoir = 1.16 x 10-3 x 20 x 20

= 0.464m3

Discharge of rectangular weir (Qweir) = Cw w(h)1.5

. = 1.83 x 1.05 x (2)1.5

. = 5.43 (m3/sec)

For 15 min it will be = 5.43 x 15 x 60

= 4887 m3

Discharge of pump will be ( Qpump) = 17.5/ H

Here H will be = (8- 1) = 7

So, (Q pump) = 17.5/7 = 2.5 m3/sec

For 15 min it will be = 2.5 x 15 x 60

= 2250 m3

Initial volume of water in the weir = 20 x 20 x 8

= 3200 m3

Water level after 15 min = Initial level + Pump Discharge - Discharge Rectangular Wier - Evaporation - Infiltration

= 3200 + 2250 - 4487- O.083 - 0.464

= 962.453 m3

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.